Median for metric spaces

• Autorzy: Nacereddine Belili , Henri Heinich
• Języki publikacji: EN

Abstrakty

EN

We consider a Köthe space $(𝔼,||·||_𝔼)$ of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.'s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ 𝔼 for all x ∈ M (we then write X ∈ 𝔼(M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ 𝔼(M) such that $||d(X,Y)||_𝔼 ≤ ||d(X,Z)||_𝔼$ for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give some applications.

Kategorie tematyczne

• 60B05: Probability measures on topological spaces
• 60G48: Generalizations of martingales
• 62F10: Point estimation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2001
• Tom: 28
• Numer: 2
• Strony: 191-209

Daty

wydano

2001

Twórcy

autor

Nacereddine Belili

• UPRES-A 6085, Analyse et Modèles Stochastiques, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France

autor

Henri Heinich

• UPRES-A 6085, INSA de Rouen, Département de Génie Mathématiques, Place E. Blondel, 76131 Mont-Saint-Aignan, France

Identyfikatory

DOI

10.4064/am28-2-6